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math.DS2026
On global Lyapunov functions being Morse
Wouter Jongeneel
Lyapunov functions have been a cornerstone of dynamical systems theory ever since the early 1900s. Moreover and akin to Morse theory, Lyapunov functions have been the key in linkin…
math.DS2025
A generalized global Hartman-Grobman theorem for asymptotically stable semiflows
Wouter Jongeneel
Recently, Kvalheim and Sontag provided a generalized global Hartman-Grobman theorem for equilibria under asymptotically stable continuous vector fields. By leveraging topological p…
math.DS2024★ 1 cited
Asymptotic stability equals exponential stability -- while you twist your eyes
Wouter Jongeneel
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the correspondi…